PYTHAGOREAN Theorem & Triples Simple Geometric Proof of Pyth. Theorem. Animation without words Why 3,4,5? Why 3 by 4 right triangle has hypotenuse 5 - EXACTLY? Does this make sense? Wrong Legs. Start with any two "wrong" legs and end up with an EXACT Pyth. Triple Pyth TRIPLES. Shows all possible triples with a given side-length. Enter a Leg in the window "Evn+2" if it is even, or in the window "Odd+2" if it is odd, and press "Enter" key. Further clicking on the corresponding button will consecutively INCREASE THAT LEG by 2 and show all possible triples. You can always enter a Leg and press "Enter" key. Or click "Restart" button to start all over. "Enter" the "Hypotenuse" in its window, and click "Hyp+1" button to check them consecutively. In all cases, multiple solutions come with bigger numbers. Here is a GAME you can play using this applet. Start from any triple (or click the buttons randomly to mess up). The goal is: By clicking the Buttons ONLY to arrive to the smallest possible triple? What is it? Can it be 3,4,5? Can it be 5,12,13? ... Can you arrive to not the smallest but any other given triple? Legs' Difference. Creating Pyth. Triples with any given difference of Legs. That difference starts with 1 by default, but clicking button "Difference +" you can increase it by 1. Clicking the "Go Higher" takes up to a higher values (above 1000). Watch he Status bar of your internet browser.